Closed form expression of tractable semi-max-type two-dimensional system of difference equations with variable coefficients

In this paper we shall examine the periodicity and formularization of the solutions for a system of semi-max-type difference equations of second order in the form xn+1=max{Anyn−1,xn−1},yn+1=min{Bnxn−1,yn−1},n∈N0, where N0=N∪{0},(An)n∈N0 and (Bn)n∈N0 are two-periodic positive sequences, and initial values x0, x−1,y0, y−1∈(0,+∞).